The importance of adequately modeling credit risk has once again been highlighted in the recent financial crisis. Defaults tend to cluster around times of economic stress due to poor macro-economic conditions, but also by directly triggering each other through contagion. Although credit default swaps have radically altered the dynamics of contagion for more than a decade, models quantifying their impact on systemic risk are still missing. Here, we examine contagion through credit default swaps in a stylized economic network of corporates and financial institutions. We analyse such a system using a stochastic setting, which allows us to exploit limit theorems to exactly solve the contagion dynamics for the entire system. Our analysis shows that CDS, when used to expand banks' loan books (arguing that CDS would offload the additional risks from banks' balance sheets), can actually lead to greater instability of the entire network in times of economic stress, by creating additional contagion channels. This can lead to considerably enhanced probabilities for the occurrence of very large losses and very high default rates in the system. Our approach adds a new dimension to research on credit contagion, and could feed into a rational underpinning of an improved regulatory framework for credit derivatives.

We look at the problem of estimating risk (Operational Risk, Credit Risk and Market Risk) and argue that risk elements, such as processes in an organization, credits in a loan-portfolio or share prices in an investment portfolio cannot be regarded as independent. This naturally leads to formulating risk models as dynamical models of interacting degrees of freedom (particles). The operational risk and credit risk problems can be cast into a language describing heterogeneous lattice gasses, in which interaction parameters and non-uniform chemical potentials have an interpretation in terms of unconditional and conditional failure probabilities. For the market risk problem, a minimal interacting generalization of the classical Geometric Brownian Motion model leads to a formulation of market dynamics that is formally similar to the dynamics of graded response neurons. We describe elements of the statistical mechanical analysis of these models to reveal their macroscopic properties.

The physics of glassy systems at low temperatures differs in striking and unexpected ways from that of their crystalline counterparts, in that thermal, transport and dynamic response properties exhibit unusual temperature variation. Atomic or molecular tunneling centers are believed to be at the origin of these phenomena, which show a remarkable degree of universality across a wide spectrum of diverse amorphous substances, ranging from window glass to polystyrene. We describe recent advances in understanding these phenomena, using a microscopic modelling approach. It has for the first time allowed to identify a mechanism responsible for the occurrence of tunneling systems, to characterize them quantitatively, and to provide a simple and transparent explanation for the unusual universality of glassy low temperature anomalies.